A toy company has developed a new toy for the upcoming Christmas season. Since this toy is considerably different from the ones it has manufactured previously, the company will need to develop a new production facility for it. Three facility sizes-small, medium, and large-are under consideration. Given the nature of the toy market, the company is unsure as to what demand level it will encounter. The preliminary analysis is to be based on the demand being low, average, or high. A small amount of subcontracting will be available, so that if the production facility is undersized it will be possible to meet some of the excess demand. The accompanying table shows the estimated profits, in $1,000s, of the various facility-size-demand-level combinations.
Demand Level
Facility Size Low Average High
Small 750 900 900
Medium 350 1,100 1,300
Large -250 600 2,000
a. Determine the best production facility size using maximax, maximin, equally likely, and minimax regret.
b. The company's initial assessment of the probabilities of the different market sizes is: P(low) = .5, P(average) = .3, P(high) = .2. Determine the production facility size that maximizes expected profits and find the expected value of perfect information.